129 



order. Four constants are introduced by integration. The 

 rod being supposed to start from a position of rest, with 

 given velocity, two of the constants vanish, and for the 

 determination of the other two we have only one equation ; 

 hence another equation is necessary. This second relation- 

 ship between the two constants is quite arbitrary, and the 

 form of the solution will depend upon what relationship we 

 choose. The physical interpretation of this arbitrary con- 

 nection of the two remaining constants is this, when we 

 set the rod in motion by an impulse we may conceive 

 any independent velocity to be simultaneously impressed 

 upon the ring. Hence the solution given in the paper refer- 

 red to is only one out of many possible solutions. If we 

 suppose the rod to start with velocity V from a position 

 of rest, and the ring to be initially at rest, the equation of 

 motion of the rod becomes 



the letters having the same meaning as in the paper 

 referred to. 



*'UIBRARV.| 



